An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is
Select the correct option:
A
$\frac{26}{49}$
B
$\frac{21}{49}$
C
$\frac{32}{49}$
D
$\frac{27}{49}$
✓ Correct! Well done.
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Solution
Let drawing a green ball is G and a red ball is R ∴ The probability that second drawn ball is red
$$
\begin{aligned}
& =P(G) \cdot P\left(\frac{R}{G}\right)+P(R) P\left(\frac{R}{R}\right) \\
& =\frac{2}{7} \times \frac{6}{7}+\frac{5}{7} \times \frac{4}{7} \\
& =\frac{12+20}{49} \\
& =\frac{32}{49}
\end{aligned}
$$
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